"Battle of a man" really makes no sense to me. "Fighting man", perhaps, but not as a female name. "Fights like a man"? Also unlikely. And the character in the Iliad is the model of a soldier's wife - loyal, supportive, warm and loving; not a bit aggressive. Perhaps it could be something like "Belongs to a man of conflict", which makes us shudder but would have been A-OK in antiquity.

People may be confused as to why a name meaning 'man' and 'battle' would be given to a woman. Allow me to clarify.

Greeks like telling stories, and that extends to names.

Basically, this name is to imply "A woman over whom men fight battles."

Which, in slightly longer explanation, "A woman so beautiful that men fight each other for her." This is all implied by the very virtue that 'men battle' is given to a woman. You kinda have to find the story in it.

It describes Helen more than Andromache, but when you realize the kind of story-telling implied by the name, it makes more sense. Names like these may be a bit odd but you just have to work a little harder to get their full meaning.